Hello, I'm new here so advanced apologies if I'm posting improperly. I am in need of some assistance on these two problems. It's been a while since I've done trig and although I know the basics I can't get the answers. Any help is appreciated...

Two fire towers are 575m apart. The first tower is 14m high, the second is 30m high. What is the angle of depression from the top of the second tower to the top of the first tower?

Richie observes the angle of elevation of an ultra-light plane to be 52°. At the same instant, the angle of elevation for Wesson is 36°. Richie and Wesson are 325m apart on level ground. How far is each person from the ultra-light plane?

Much Obliged. (Bow)

Jan 21st 2011, 05:46 PM

ragnar

Here's my stab at it, though the numbers seem weird:

So the difference in height is 16m so we're looking at a right triangle with base 575 and height 6. We could do this a few ways, but let's do something pretty standard: Find hypotenuse, $\displaystyle \sqrt{(575)^{2}+16^{2}} = 575.223$ which is what we'd expect since the base is so long and height so small. $\displaystyle \sin(\theta) = \frac{575}{575.223} \Rightarrow \theta = \sin^{-1}\Big(\frac{575}{575.223}\Big) \approx 88.4$.

The angle of depression is 90-88.4 = 1.6 degrees.

I'm tired so hopefully someone else can take over or you can see how I did it and reproduce it for the second problem.

Jan 21st 2011, 06:29 PM

Prove It

Why bother working out the hypotenuse, when you can use the Tangent Ratio?

Jan 21st 2011, 06:45 PM

ragnar

Because that's how I ROLL. And it was the first thing that came to mind, and it appealed to the most basic concepts so I figured it'd be easy to follow. And it's how I ROLL.